Adam Kaminski (Iowa State/ Ames Lab): Competing ground states in cuprates: disentangling Cooper-pair formation above Tc from the pseudogap state

Introduction and Background

Adam started his talk introducing the ARPES technique: photons are incident in the sample and, as a result, electrons are emitted. These electrons are then detected and, from their momentum and energy, important information about the material can be extracted. In particular, Adam explained that the quantity measured by ARPES is the spectral function, multiplied by the Fermi function and the proper matrix element. He presented the experimental details of the technique and the instrumentation his group has been using to obtain data.

Adam also showed examples of ARPES intensity plots of doped BSCCO samples, explaining how one can extract the Fermi surface and the band structure from them. He also presented cuts in the intensity plot, which can give either EDCs (energy distribution curves) or MDC (momentum distribution curves). In superconducting (SC) samples, the SC gap can be extracted from the EDC, as a sharp peak appears below Tc.

Q (Andriy Nevidomsky): What is the difference between the data extracted by ARPES and STM?
A: They have similarities, but ARPES is able to give information about momentum dependence, particle lifetime.

Now, Adam is explaining how one can extract only the spectral function from the EDC data, eliminating the Fermi function factor. There are two possible approaches: divide the EDC by the Fermi function or symmetrize the curves (the latter is due to Mike Norman). Adam further explained the details of the symmetrization procedure and its suitability to extract gaps amplitudes.

Q: Does ARPES measure surface or bulk properties?
A: Surface properties, but in anisotropic materials like the cuprates they are expected to be similar.

[A discussion about particle-hole symmetry and the ARPES spectrum is taking place now, involving Andy Schofield, Andrey Chubukov and Adam]

Before going to the main topic of his talk, Adam explained that samples have a finite "laboratory lifetime", since they age due to CO2 absorption when vacuum is less than perfect.

Pseudogap in the cuprates

After showing us spectra from the cuprate SC Bi2212, Adam posed one of the main points of his talk: is the pseudogap in the cuprates a friend or a foe of superconductivity? He presented two different approaches in the current literature: one of them considers that the pseudogap state is due to pre-formed pairs (Emery and Kivelson). The other approach considers that the pseudogap is an ordered state (such as DDW, ordered dimers, CDW, persistent currents). Adam's proposal is to use highly precise ARPES data to shed light on this discussion.

The first set of data presented by Adam showed the angular dependence of the spectrum gap (extracted from the EDC) in OP (optimally doped) Bi2201 for a given temperature below Tc. The data, Adam argues, show significant deviations from a pure d-wave behavior. His proposal is that the spectral gap has actually two contributions: one from the actual SC gap and another from the pseudogap.

Still focusing on the spectral gap, Adam showed its detailed momentum dependence across the phase diagram. After comparing the spectral gap below and above Tc for UD (underdoped), OP (optimally doped) and OD (overdoped) samples, Adam showed that it has a very unusual temperature dependence, which is non-monotonic - another evidence for two gaps, he says. With these results, Adam motivates that the individual spectral weights, instead of the spectral gap, should be investigated in details, in order to obtain independent information about the PG (pseudogap) and the SC gap.

His group studied Bi2201 samples, focusing first on the properties of the spectral function at the antinode (i.e., fixing the momentum). They associate the coherent peak to the SC state and itsweight, to the superfluid density (he points out that no theoretical model gives this correspondence, it is an empirical observation). On the other hand, the loss of spectral weight at the Fermi level is a hallmark of the pseudogap, Adam says. With these two energy scales - namely, the coherent peak weight and the loss of spectral weight at Ef - Adam extracts independently the spectral weights associated to the PG state and to SC.

Now, Adam is presenting a systematic study of these two spectral weights below Tc for UD, OP, and OD samples across the Fermi surface. In particular, starting from the nodal point, he probes the weights along the Fermi surface by 45 degrees, until the antinodal point is reached. He showed plots with the PG weight increasing at the expense of a decrease in the SC weight across the Fermi surface (for the three different doping levels). Plotting these two weights in the same figure, one in each axis, Adam argues that his data imply an anti-correlation between them, concluding that the pseudogap is a foe of SC - i.e. they are competing states. He warned that these are indirect measurements, reflecting spectral properties. To support his interpretation, he showed penetration depth data, which is a direct measurement of the superfluid density.

Pre-formed pairs in the PG state

Adam has now switched to the next topic of his talk. He first presents Nernst effect data, which find local pairing in the cuprates above Tc. To probe local pairing with ARPES, Adam's proposal is to use the spectral function to extract the Fermi surface density of states, which should be sensitive to pair-breaking effects and local pairing. He also presented STM data, which shows evidence of SC patches above Tc.

Using the EDCs obtained by ARPES, Adam's group extracts the spectral weight at Ef (the Fermi energy). A linear behavior of this weight with temperature is observed at higher temperatures, which he associates to the PG. The deviation of the Ef weight from linear in T behavior, according to Adam, marks the onset of another feature, which he claims is associated to local pairing. The energy scale associated to this deviation, which is above Tc but below T* (the PG onset temperature), is called Tpair.

Now Adam is showing a set of data for various UD and OD Bi2201 samples, focusing on the Ef weight at the antinode, where the SC gap is expected to be larger. He further presents several plots of this Ef weight as function of temperature for various dopings.

Q (Piers Coleman): Are the vertical lines at Tpair also extracted from resistivity? Are they associated to T*?
A: No, they do not appear in the resistivity, which only shows T*, not Tpair.

Adam argues that one can separate the Ef weight contribution due to the PG by extrapolating the high-temperature linear behavior (Wpg). The rest of the weight at the Fermi level is then associated to pairing, Wpair. Adam presents plots showing how Wpair and Wpg depend on temperature for different doping levels. He is able to scale all the different temperature-dependent Wpair measurements in a single plot, and suggests that they obey an universal scaling relation. Adam interpretation is that Tpair sets the temperature where pairs are first formed, which is rather below T*, but above Tc. To confirm his explanation, he also presented the evolution of both Wpair and Wpg across the Fermi surface.

Adam compares his ARPES data with NMR, resistivity, neutron and Nernst effect data. Specifically, he compares the phase diagrams extracted from these different techniques, and the corresponding values of T* and Tpair. He argues that neutron and Nernst data are also sensitive to Tpair, while NMR and resistivity are sensitive to T*. In Adam's picture, Tpair marks the onset of strongly phase-fluctuating SC pairs, which only acquire phase coherence below Tc. Between Tpair and T* (the PG onset temperature), there would be no pre-formed pairs. He mentions that some theoretical models are able to correctly capture the importance of these two fluctuation modes (phase and amplitude).

To finish his talk, Adam poses the question: what is the relation between his results and the checker-board order seen by STM? He compares the STM data with ARPES and argues that the pseudogap energy scales extracted from both methods are in good agreement.

Discussion

Q (Zlatko Tesanovic): Take the pairs and freeze them in a checker-board lattice, while others pairs wander around. Is the spectral signature of this configuration different than the one seen by ARPES?
A: Cannot exclude other scenarios consistent with the data, but he can certainly say that below Tpair there is local pair formation.

Q (Andrey Chubukov): The position of the peaks is not necessarily proportional to the gaps when disorder and finite lifetime are present. Explicit calculations would be interesting. He also asks Adam to compare his results with measurements from other ARPES groups, which claim to see perfect d-wave gap.
A: Both results are right, the energy scales probed are different.

Comment (Lu Yu): Emphasizes the important result that, in momentum space, the additional spectral weight starts at the end of the Fermi arcs and them grows towards the arcs.

Comment (Piers Coleman): Adam's data shows anisotropy in the momentum space. On the other hand, we heard about nematic order [Keimer's data, earlier talk], with rotational anisotropy in real space. Is there a unified picture that takes into account both real space anisotropy and momentum space anisotropy?

Q (Zlatko Tesanovic): Asks about the fact that different ARPES groups apply different symmetrization procedures to the EDCs.
A: The results presented in the talk do not depend on the symmetrization procedure.

Comment (Andrey Chubukov): Comments on Piers question and on what different experiments could be probing.

Comment (Adam Kaminski): Adam comments on the relation between nesting of the Fermi surface, the antinodes position and the observed anisotropy of the order parameter.

Q (Cecilia Ventura): [Blogger did not hear because was typing the previous questions]
A: Both ARPES and STM measurements are affected by important matrix elements.